Question

A block of mass $m$ is attached to one end of a mass less spring of spring constant $k$. The other end of spring is fixed to a wall. The block can move on a horizontal rough surface. The coefficient of friction between the block and the surface is $\mu$. Then the compression of the spring for which maximum extension of the spring becomes half of maximum compression :

• A. $\frac{2mg\mu }{k}$
• B. $\frac{mg\mu }{k}$
• C. $\frac{4mg\mu }{k}$
• D. none of these

Answer 1

Answer: (C)

$\frac{4mg\mu }{k}$

$E_i-E_f=\text{Work done against friction}$
$\therefore \frac{1}{2}k{x}^2-\frac{1}{2}k{\left(\frac{x}{2}\right)}^2=\mu mg(x+\frac{x}{2})$
$\therefore x=\frac{4\mu mg}{k}$